Heitler-London configuration

Fig. 1 Energy diagram that illustrates the mixing of the Heitler-London configuration, R- -X, with the zwitterionic configuration, R+ X, to generate ground (S0) and excited (S,) states of the R—X bond...

Fig. 3.7 The Heitler-London configuration A(1) B(2) and A(2) B(1) (a) and (b) respectively, where 0A and represent the atomic 1s orbitals centred on atoms A and respectively, and 1 and 2 represent the coordinates of the two (indistinguishable) electrons, (c) The molecular orbital basis function in the singlet state where electrons 1 and 2 have opposite spin, (d) The up and down spin eigenfunctions corresponding to local exchange fields of opposite sign on A and B.

Fig. 3. Interacting fragment configurations (IFC) for reactant and product diabatic wavefunctions for a 2 + 2 addition, la—Id are no-bond reactant-like configurations while II is a triplet-triplet Heitler-London configuration.

In this study the three n orbitals of allyl and the Is orbital of H at infinite separation have been taken as the valence orbitals (see Fig. 10). This choice provides a correct description of the motions investigated here since it allows proper dissociation of both propene and a trimethylene-like species into allyl radical plus a hydrogen atom. An MC-SCF computation of a planar allyl radical plus the hydrogen atom at 20 A has shown that the ground and first excited states of this system are mainly described in terms of the three Heitler-London configurations shown in Scheme VI ... 

Calculations in which the orbitals used are restricted to being centered on only one atom of the molecule. They are legitimately called atomic orbitals . Treatments of this sort may have many configurations involving different orbitals. This approach may be considered a direct descendent of the original Heitler-London work, which is discussed in Chapter 2. 

It is dear, therefore, that as the atoms are pulled apart the Hartree-Fock MO solution does not go over to that of two neutral-free atoms H°H°, but instead goes over to a mixed configuration, schematically represented by [2H°H° + H+H" + H H+]. Since the energy cost for the ionic configuration is / — A = (13.6 — 0.8) eV = 12.8 eV, the Hartree-Fock MO solution dissociates incorrectly to +6.4 eV rather than zero (We have assumed the Hartree-Fock treatment of H is exact.) The Heitler-London VB solution avoids this problem by working with only the covalent configurations in the first square bracket of eqn (3.37), so that it dissodates correctly. 

The original Heitler-London treatment with its various extensions was a VB treatment that included several configurations, e.g., the total wave function is a sum of terms with spatial functions made up of different subsets of the orbitals. This is the essence of multiconfiguration methods. The most direct extension of this sort of approach is, of course, the inclusion of larger numbers of configurations and the application to larger molecules. The computational power allowed calculations of this sort. 

We use these in a single Heitler-London covalent configuration, i4(l)i (2) + 5(1) 4(2), and calculate the energy. When R - oo we obtain E = — 1 au, just as we should. At R = 0.741 A, however, where we have seen that the energy should be a minimum, we obtain E = —0.6091 au, much higher than the correct value of -1.1744 au. The result for this orthogonalized basis, which represents no binding and actual repulsion, could hardly be worse. 

Here the first two determinants are the determinantal form of the Heitler-London function (eq 1), and represent a purely covalent interaction between the atoms. The remaining determinants represent zwitterionic structures, H-H+ and H+H, and contribute 50% to the wave function. The same constitution holds for any interatomic distance. This weight of the ionic structures is clearly too much at equilibrium distance, and becomes absurd at infinite separation where the ionic component is expected to drop to zero. Qualitatively, this can be corrected by including a second configuration where both electrons occupy the antibonding orbital, Gu, i.e. the doubly excited configuration. The more elaborate wave function T ci is shown in eq. 4, where C and C2 are coefficients of the two MO configurations ... 

Shifted ST0-6G electronic energies ( = -E - 36.0 a.u.), and VB structural weights for resonance between VB structures I-IX. Structures VII-IX involve (2s)1(2p)1, (2s)1(2p)1 and (2p)2 configurations for the LiW. The wavefunctions for the electron-pair bonds involve Heitler-London AO formulations. 

We focus on the three-body forces in Fig. 5.21 where the SCF portion is compared with its components extracted before (Heitler-London, HL) and after (deformation, def) the wave functions of the monomers are perturbed by one another. It is apparent that the latter SCF-def forces are largely responsible for the anisotropy of the SCF three-body terms. The Heitler-London component is weaker, and resembles a mirror of SCF-def, with a maximum where SCF-def contains a minimum. The extremum at 20° corresponds to a configuration... 

Let us note that the above assumption was used by Frenkel and Davydov (9)-(11) by constructing the wavefunctions in the Heitler-London approximation in its simple version. In their theory only the part of the intermolecular interaction was taken into account, which causes the excitation transfer from one molecule to another, and not those which gives the mixing of molecular electronic and vibronic configurations. 

Calculations of the lowest excitonic states in anthracene were performed by Silbey et al. (74), Craig (12), Fox and Yatsiv (75), Davydov and Sheka (76), and Claxton (77) within the Heitler-London approximation. In the papers by Silbey et al. (74), Craig (12), Fox and Yatsiv (75), and Claxton (77), only the states k 0 were considered, and the mixing of molecular configurations has been taken into account. Davydov and Sheka (76) have neglected the mixing of molecular configurations, but for some directions of the wavevector they obtained the form of excitonic bands by means of the Heitler-London approximation. 

Any two-state VBSCD can be transformed into a VBCMD where the Heitler-London (HL) and ionic VB structures are plotted explicitly as independent curves, instead of being combined into state curves [11]. As a rule, ionic structures, which are the secondary VB configurations of polar-covalent bonds, lie above the covalent Heitler-London (HL) stmctures at the reactant and product geometries, and generally they cross the two HL stmctures above their own crossing point. In many cases, the ionic curve is low enough in... 

The procedure of taking a linear combination of atomic orbitals, which we have considered with respect to the H2 molecule, is very fruitful when applied to other covalent bonds. Consider, for example, the hydrogen fluoride molecule, HF, formed from a hydrogen atom with one electron in the Is state and a fluorine atom with an electron configuration of ls 2s 2p. Fluorine has an unpaired 2p electron, and we can form a wave function of the Heitler-London type by making use of the atomic orbitals for this 2p electron and for the Is electron in the hydrogen atom ... 

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